Can I sue a shipping company for not honoring an insurance claim?

I sent my belongings from a shipping store in the USA to Mexico where I'll be living for the next 6 months. I got extra insurance on one box and the other boxes had $500 of insurance included. The boxes were packed by me with plenty of bubblewrap but had to be repacked by the store and then again after customs inspection in Mexico. I was present for the inspection and customs did not damage anything. It had to be repacked AGAIN by the shipping company to assess a value for customs. Each time they packed my stuff, it was done badly and as a result, my belongings are damaged. My insurance claim was denied on the basis of not having double walled boxes or enough bubblewrap. Nobody told me when I sent it that the boxes were inadequate. The problem was that they repacked items without the included bubblewrap around them. I spent $75 on bubblewrap so it was more than enough. Again, the shipping store, and the same shipping company repacked my boxes badly, and insurance was denied. Can I sue?